What is the general solution for sin(x)=-0.397 ?

The general solution for sin(x)=-0.397 is x=-0.40824…+2pin,x=pi+0.40824…+2pin

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sin(x)=-0.397

sin (x) = - 0.397

x = - 0.40824 \dots + 2 πn, x = π + 0.40824 \dots + 2 πn

Degrees

x = - 23.39076 \dots^{\circ} + 36 0^{\circ} n, x = 203.39076 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = - 0.397

Apply trig inverse properties

sin (x) = - 0.397

General solutions for

sin (x) = - 0.397

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (- 0.397) + 2 πn, x = π + arcsin (0.397) + 2 πn

x = arcsin (- 0.397) + 2 πn, x = π + arcsin (0.397) + 2 πn

Show solutions in decimal form

x = - 0.40824 \dots + 2 πn, x = π + 0.40824 \dots + 2 πn

\frac{2 tan ( x )}{1 - tan ^{2} ( x )} = 1

2 cos (x) \cdot tan (x) - 1 = 0

2 - 2 cos (θ) = - 6 cos (θ)

tan (θ) = \frac{- 372.688}{- 831.628}

1 + 2 sin (x) = 1

What is the general solution for sin(x)=-0.397 ?
The general solution for sin(x)=-0.397 is x=-0.40824…+2pin,x=pi+0.40824…+2pin